Algebra Know-It-ALL

Practice Exercises

This is an open-book quiz. You may (and should) refer to the text as you solve these problems.

Don’t hurry! You’ll find worked-out answers in App. B. The solutions in the appendix may not

represent the only way a problem can be figured out. If you think you can solve a particular

problem in a quicker or better way than you see there, by all means try it!

1. Using the S/R table method, morph this into standard form for a first-degree equation
   in one variable:
   4 x+ 4 = 2 x− 2


2. Using the S/R table method, morph this into standard form for a first-degree equation
   in one variable:
   x/3= 6 x+ 2


3. Using the S/R table method, morph this into standard form for a first-degree equation
   in one variable:
   x− 7 = 7 x+x/7


4. Using the narration method, morph this into standard form for a first-degree equation
   in one variable:
   x/3+x/6= 12


5. Solve, in no more than two steps each, the standard-form equations you derived in
   Probs. 1 through 4.


6. When you multiply a certain number by 2, then add 8 to that product, and divide that
   sum by 4, you get −1. Find the number by devising a first-degree equation in x, and
   then solving for x.


7. Suppose we take a certain number, and then subtract 1/10 of itself. After that, we
   divide the result by 2, and end up with 135. Find the number by devising a first-degree
   equation in x, and then solving for x.


8. Bill weighs 10 kilograms (kg) more than Bruce, and Bruce weighs 5 kg more than
   Bonnie. The combined weight of all three people is 200 kg. What does each person
   weigh?


9. Imagine that we have a motorboat with a maximum water speed (the speed relative to
   the water it’s floating on) of 18 miles per hour (mi/h). We make a trip upstream from
   our cabin to our cousins’ cabin, a distance of 18 miles (mi), running the boat at top
   speed all the way. The trip takes 1 hour and 12 minutes (1 h 12 min). We would expect
   it to take exactly 1 h if there were no current in the river. But the current, which we
   were fighting, slowed us down. How fast was the river flowing? Assume that the river
   flowed at the same speed all during our journey.


10. Assuming the river keeps flowing at the same speed as we determined when we solved Prob. 9,
    and our boat’s water speed is always 18 mi/h, how long will it take us to travel downstream
    from our cousins’ cabin back to our own? Here’s a hint: The travel time (in hours) equals the
    distance traveled (in miles) divided by the constant speed (in miles per hour).

Practice Exercises 207